The curve $C$ is given by the equations

1. Show that

   $$\frac{dy}{dx}=\frac{ax}{by}$$

   for some $a,b\in \mathbb{N}$.

2. Find a Cartesian equation for $C$.

For (b), try squaring $x$ and $y$. Recall that $1+{\tan }^2(t)={\sec }^2(t)$.

Give the value of $a+b$.